Question about Maclaurin series - calculus

[andydan1060]

Homework Statement

Find the Maclaurin series of the function https://webwork.wustl.edu/webwork2_files/tmp/equations/87/63afd4b6f3566e2a90aa420dc5d1821.png
c_3 =
c_4 =
c_5 =
c_6 =
c_7 =

Homework Equations

The Attempt at a Solution

(8x^2)[(9x) - (9x)^3/3! + (9x)^5/5! - (9x)^7/7! + ...]

I got c_3 = 72, which is correct, and c_5 = (8x^2)[(9x^3)/3!] = 5832/3! (coefficient)

Apparently that's wrong and it's supposed to be -116640/(5!).

What did I do wrong? Thanks!

 

[PeroK]

Are you not just muddling up which coefficient is which? If you've got 1/3! and the answer has 1/5! then those are different coefficients.

 

[Delta2]

Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?

 

[andydan1060]

Homework Statement

Find the Maclaurin series of the function https://webwork.wustl.edu/webwork2_files/tmp/equations/87/63afd4b6f3566e2a90aa420dc5d1821.png
c_3 =

Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?

It's supposed to be
c_4 =
c_5 =
c_6 =
c_7 =

Homework Equations

View attachment 82633

The Attempt at a Solution

(8x^2)[(9x) - (9x)^3/3! + (9x)^5/5! - (9x)^7/7! + ...]

I got c_3 = 72, which is correct, and c_4 = (8x^2)[(9x^3)/3!] = 5832/3! (coefficient)

Apparently that's wrong and it's supposed to be -116640/(5!).

What did I do wrong? Thanks!

Isnt c4 supposed to be the coefficient of x^4 which is zero in this series?

It's supposed to be c_5, not c_4, sorry.

 

[PeroK]

It's supposed to be c_5, not c_4, sorry.

First, your coefficient should have a minus.

Second, why do you think your answer and the answer given are different? Just because they look different doesn't mean they are!

 

[Delta2]

Well PeroK is right, doing the calculations it turns out that 5832/3!=116640/5!. However i wonder if your teacher wanted you to do this assignment by manually calculating up to the 7th derivative of 8x^2sin(9x) and evaluating the derivatives at 0.

 

[PeroK]

Well PeroK is right, doing the calculations it turns out that 5832/3!=116640/5!. However i wonder if your teacher wanted you to do this assignment by manually calculating up to the 7th derivative of 8x^2sin(9x) and evaluating the derivatives at 0.

I suspect that since we have the coefficient of $x^5$, whoever gave the answer preferred to have $5!$ in the denominator.